To isolate the benefit of noise injection, we adapt the approach of [1]}, [2]} to our setting to show that the Gaussian noise injection procedure in NFM robustifies manifold mixup in a probabilistic sense. At its core, this probabilistic notion of robustness amounts to making the model locally Lipschitz with respect to some distance on the input and output space, ensuring that a small perturbation in the input will
not lead to large changes (as measured by some probability metric) in the output. Interestingly, it is related to a notion of differential privacy [3]}, [4]}, as formalized in [5]}.
